## Thursday, 18 February 2010

### Maths is so arbitrary

I like some maths, but I've always found the basic entity of mathematics a trifle scary. Not because it's difficult, but because it's arbitrary. When you do science, what you say has to be based on the world around us. You can always check things against reality. However, mathematics is an isolated world. You can make a totally arbitrary set of statements, and as long as they are self-consistent, then they're okay. Human beings make up the rules in maths, and that's the scary bit.

Take one simple example - prime numbers. Until the 1800s, the number 1 was mostly considered to be a prime number. After all it has no divisors other than itself and 1 - so it should be. But then it was decided that one was too unique (!) - its strange properties like 1x1=1 made it somehow not a real prime number. So now 1 is excluded from the list and prime numbers start at 2. That's fine, that's the rule - but it is painfully arbitrary. If they wanted to, someone could decide that 2 wasn't a prime number either, as every other prime number is odd. They haven't yet, but it could happen.

Science may be weird and wonderful. And it mostly depends on maths - so some maths I'm very happy with because it is tied into reality. But the work of some pure mathematicians gives me the willies.